Random Factors in Gaming

Die Siedler is something of a phenomenon, when it first came out
it took the gaming world by storm. Everyone was playing it, it won
all the awards and people just couldnít get enough of it. Lately,
the game seems to have lost some of its appeal, however. Personally
I think itís a case of a game simply being overplayed but many
mention that theyíve lost interest because the game is "too
random". Its pretty easy to see where this idea comes from,
after all the game does use dice as its driving mechanism. The
player that receives the lionís share of the rolls IS more likely to
win but does that mean that the game is "too" random?
Certainly thereís a random element and thereís been plenty of
anecdotal evidence of a game that was won purely by a series of
lucky die rolls. In spite of this Iím not sure that Iíd want to
classify the game as luck based. Some have suggested that any skill
in the game is in the initial placement of settlements, the game is
one-third skill (the initial placements) and two-thirds luck (the
rest of the game). Iím not sure that I agree totally with this
although my opinion may have something to do with my record:

Iíve played the game 21 times at my weekly gaming session (from
which the results are recorded) and Iíve managed to win a total of
16 times. These were all 4-player games. I suppose its partly ego
that leads one to the conclusion that success in a game is
attributable more to your skill and intelligence than anything as
unseemly as luck.

Still, thereís something to this argument. You would expect, in a
game of pure skill, that the better (i.e. more "skillful")
player would win most, if not all, of the time. If this is so then
it seems a natural conclusion that a games "skill" level
could be gauged by the regularity with which certain players win.
Unfortunately, this "test" has a couple of problems,
primarily the fact that you have two unknown (non-quantifiable
really) variables: the degree to which the game is
"skill-based" and the actual skill of the players.
Consider world championship Chess, usually played over a series of
20 or so games with the final result often in the neighbourhood of
11 to 9. Compare this with a "Roll the Dice" contest
which will usually result in a similar final score. I think it safe
to say that Chess is much more skill based than "Roll the
Dice" so these results donít really tell us much in and of
themselves. At the very least they donít confirm what we already
suspect, which is that Chess is a more skillful game. Even with this
misgiving I still think that itís a useful test, a rough indication
of a games level of skill, even if it is a rather loose one. In any
event why do certain games feel more random to some players than
others? Maybe it would help if we had a look at some of the
different random elements in games.

The most obvious element is the use of physically unpredictable
devices such as dice. This would also include such things as
spinners or exotic items such as the devil's pot from In Teufelís
Kuche. (If you havenít seen it its a small pot belly type stove with
a button on top. Players alternately press the button until the
devil lurking inside pops out, very cute!) Basically this includes
anything that has a physical mechanism thatís not predetermined.

Two related, and very commonly used randomizing elements, are
cards and tiles. A little distinction is necessary here. What Iím
thinking of is a closed, known set of items and these can take many
forms. In Bridge you know exactly what cards are in the deck. In
Acquire you know that there is a single tile for each space on the
board. In Settlers you know that there are four sheep, wood and
wheat hexes, three brick and ore hexes and one desert. The random
factor in each of these is in how the cards are distributed, the
tiles drawn or the hexes placed. I should also note that these items
are not necessarily random influences. The commodity cards in
Settlers arenít, theyíre simply an accounting tool. The tiles in
1830 arenít a random element as theyíre chosen rather than blindly
drawn. (I should also note that cards can be considered as a
"dice-type" randomizer in certain circumstances. If you
are drawing and then replacing a card from a fixed, constant
deck then its much closer in function to dice than if you are
drawing and discarding or keeping a card. The specific
example Iím thinking of is Hase und Igel where the Hare cards are
constant in number; you draw one, follow its instructions and then
replace it in the deck. In fact, the original English version uses
dice to perform the same task, albeit slightly modified.)

Another random element is the seating/turn order. In a two-player
game this is usually simply a case of who has the first move,
normally itís an advantage to go first. In the case of games that
have unequal sides (such as wargames like Hannibal: Rome vs.
Carthage) its also a matter of who plays which side. In multi-player
games its a little more complicated. The order in which you are
sitting can have a great impact on your strategy in a game. In
Illuminati its generally better to ally yourself with someone
sitting next to you as you will have back to back turns. In Show
Manager itís very important that you try to stage a different show
than the person to your right otherwise theyíll be hiring the actors
that you want. This is in addition to any advantage of going first.
(Note also that its not always an advantage to go first, some insist
that going last in Die Siedler is better as you get to place two
settlements at once. Also the first two players in Durch die Wuste
only get to place a single camel instead of two.)

The final element (that I can come up with at least) is the
players themselves. What Iím thinking of is the mechanism (if there
is one) that causes a player to perform a certain action. It would
be quite easy to argue that there is no randomness in this at all
and I donít necessarily disagree with that line of thought. In any
case such a debate is not likely to lead to any useful conclusions
and is best left to another forum. I simply include its mention for
completeness and that some of my opponentsí moves sure as hell SEEM
random to me!

I suppose that each one of these elements is going to bother
every player to a different degree. A lot of this is going to have
to do with how a game "feels" to us. There are going to be
people that have a problem with any game that includes dice.
Equally, there will be players for which cards are too great a
random factor. I believe that itís possible for any of these
elements to be modified to an acceptable level. (I donít think you
can actually modify my final element, the players themselves, but
weíll ignore that.)

The unpredictability of dice or cards can be modified in many
ways. In Die Siedler the dice are added together which gives a bell
curve distribution. The game is less random because there is greater
predictability in the commodity rolls than if it was a single die
that was rolled. Any particular result is still random of course but
you will expect more 6ís to be rolled than 10ís over the course of
the game. This is another important concept: as you increase the
number of die rolls you will get closer to the expected average. I
often hear someone make the comment that they donít like a
particular game because "Itís too random, thereís too many dice
rolls." This might at first seem to be a logical argument but
it ignores the law of probability that as you increase the instances
of a random event you are more likely to get an expected average. To
illustrate this, consider a dice contest between Danny & Roger:
A single six-sided die is rolled. On a 1 or 2, Danny wins otherwise
Roger wins. If the "game" is a single throw of the die
Danny will expect to win 1 out of 3 times. However, if the game is
the best out of three rolls Danny can only expect to win 7 out of 27
times which is slightly less than 1 out of 3. This is a result of
Rogers advantage in the game. As we increased the number of rolls
the random effect became less of a factor and the advantage became
more significant. The point is that the more dice rolls in the game
the less pronounced their individual effect. There are, as always, a
couple of points to note about this specific example. First is that
each roll had exactly the same effect on the outcome as all others.
In a real game certain rolls are more important than others, for
example, in Titan your movement roll is far more important than any
attack roll. Also, the order of the rolls was not significant
whereas in a real game the effects of earlier dice rolls often
affect later ones. e.g. In Titan if you roll lots of hits at the
start of a battle your opponent will have fewer attacks to make on
subsequent turns and so, in general, it is better to roll well
earlier. So, one way that you could decrease the luck in a game that
uses dice, such as Die Siedler, would be to increase the number of
individual rolls in the game. This is probably going to be somewhat
difficult to actually implement in a game outside of the design
process. Another, more easily added method would be to actually
remove the dice from the game and there are a couple of ways this
could be accomplished. One particular method Iíve heard proposed for
Die Siedler involves a set of 36 cards with each card showing a
number from 2 to 12. The total number of each card listing a
particular result would match a standard distribution so that you
would have one card showing a "2" and six cards showing a
"7". These cards would then be used in place of a die roll
to determine which commodities appear. There are even multiple
methods by which you could employ them; one is to have a single
common shuffled deck from which you drew a card. Another would be
for each player to have their own decks and they would choose which
card to play each turn. Iím not so sure that the final results would
be all that much different in a game like this but it would
eliminate the rare games in which a wild and unusual set of rolls
determined the outcome.

In the case of cards, their unpredictability can be modified as
well. First consider the case of a game where players draw from a
face down deck. A common method of reducing this random effect is to
have several face up cards beside the stack. A player now has the
choice of choosing one of the face up cards or drawing blind from
the deck. Alan Moon often employs this so-called
"drafting" method in his games and it works very well. A
particular bonus of this method is that itís very easy to tailor it
to a particular level, if you want less predictability, have fewer
face up cards, if you want more, increase the number of face-up
cards. Simple. Another way of reducing the random effect of drawn
cards (at the design level anyway) is to reduce the variety of
cards. In Euphrat & Tigris there are only four types of tiles so
while you can never be sure exactly what youíre going to get you
have a pretty good idea.

What about the randomness in turn order involving games where
itís advantageous to go first? In these cases a bidding mechanism
can be introduced where players compete for this right. In the case
of two player games you could play a pair of games with the
cumulative score determining the winner. Unfortunately thereís not
much that can be done for the "randomness" of other
playersí strategies. As there are many that would argue that this
isnít really a random factor anyway its probably best to take the
practical approach and resist any attempt to "fix" it.

As a practical exercise letís have a look at some real games,
specifically Reiner Kniziaís so called "tile laying
trilogy", Euphrat & Tigris, Durch Die Wuste and Samurai.
What random elements are there?

E&T: The only random elements are the tile draw and the
seating order. Implementing an above-described "drafting"
tile draw would reduce much of the luck in the present system.

DdW: The only random elements are the seating order and the
initial setup. (Iím assuming a four-player game where each player
has all five caravans in play. In a five player game, where each
player only has four of the five caravans, it depends on how you
remove each players "extra" caravan. Obviously if you
determine it randomly thatís another random element.) As a
particular layout does not necessarily favor one player over another
Iíd suggest that thereís very little luck involved at all. Thereís
recently been some discussion on the Internet about how to conduct
this setup and a couple of people have suggested that the board be
setup as follows: Each player, in order, chooses an oasis or
waterhole token and places it on the board. Placement proceeds
clockwise around the table until the board is complete. I really
doubt that all this extra effort is worth it in the end but each to
his own. If the turn order was seen as a problem this could probably
be solved by implementing a bidding system for who goes first. There
are a couple of ways that you could increase the luck in the game:
Instead of choosing which camels to place you secretly draw from one
of five concealed bags. The game ends when one bag is empty. Instead
you could have 6 hidden camels behind a screen, you may play any of
them and you replenish your "hand" to 6 from a common
stock. Game ends when 12 oasis tokens have been awarded.

Samurai: Random elements are the initial setup, random draw of
tiles and seating order. As with DdW you could solve the initial
setup "problem" with a similar placement mechanism. I
donít think thereís a bidding system that would work for determining
the first player though. The only thing I can come up with would be
something along the lines of bidding how few of your initial 5 tiles
you get to choose. I doubt that this would work all that well in
practice. The random draw is interesting to me especially when
compared to E&T. On the one hand Samurai seems less random due
to the fact that everyone will get the same distribution of tiles.
On the other hand there are more varieties of tiles, which makes it
less likely that youíll draw the one you want at the right time.
Which is more random? The biggest complaint Iíve heard about E&T
was the random draw of tiles and I can understand this somewhat,
itís very frustrating if you never draw those damn green tiles!
There are a couple of tactics that can be used to overcome this
however and I personally feel that this is what separates the good
players from the bad. Iím not sure if Knizia designed the tile draw
in Samurai as a direct response to this but it does seem that people
have fewer problems with it.

All three of these games exhibit some degree of luck. I think its
safe to say that DdW has the least of the three but Iím not sure how
Iíd rank the other two. In Samurai I often have to speculate whether
or not Al has his 4 Buddha available. In E&T the equivalent is
speculating if he has 3 red tiles. For this situation Samurai
"feels" more random to me but perhaps Iím in the
minority?

There are also many games where a certain degree of randomness is
"built in". The best, fictitious example I can think of is
Chess-Dice. (Which I first read of in a post to rec.games.board by
David desJardins. Iím not sure if its his original idea or not.) The
game is played in two parts. First a regular game of Chess is
conducted and then each player rolls a single die. If there was a
winner in the Chess game, that is, the game was not a draw, then
that player adds 1 to his roll. Highest roll wins. I think everyone
would agree that the game is pretty random even though it also
rewards skillful play. In fact, there is just as much depth and
skill inherent in Chess-Dice as there is in regular Chess. The big
difference though is that the rewards for skillful play are not as
pronounced in Chess-Dice as they are in Chess. This is fairly
obvious in this case but Iím only using it to make a point. The
point being that some games have the appearance of requiring great
skill but the game does not actually reward that skill as much as
others. There have been a couple of situations where random events
have totally ruined a game for me. The most obvious ones have been
games that have a "switch positions" rule. Twice Iíve been
the victim of this, the first in a PBEM game of Cosmic Encounter,
the second in Flying Carpet. Iíd argue that these rules make the
games as ridiculous as that of Chess-Dice, a single random event
overwhelming any skill that the game requires.

So, back to the original question (was it the original
question?), why do some games feel more random to some players than
to others? It could be a simple case of closely matched opponents.
Most people play with the same group of people and its quite likely
that they are of approximately the same level of skill. This is
going to have the effect of emphasizing any luck inherent in the
game. It could also be the small number of times a game has actually
been played by an individuals. Even the 21 games that Iíve played of
Die Siedler are probably not statistically significant to make any
claims about my ability in the game. Also, if youíve only played a
game two or three times any aberrant events are more likely to cloud
your opinion. So, once again Iíve rambled on about a subject but
have I actually stated anything useful? I suppose thatís for others
to decide but I think the most important point Iíve made is that
itís usually possible to fine-tune a game to your particular
luck/skill ratio. As always Iíd be interested in hearing any
thoughts on this subject.